High-order averaging schemes with error bounds for thermodynamical properties calculations by MD simulations
Résumé
We introduce high-order averaging formulae for the computation of statistical averages on the basis of the numerical simulation of long-time molecular dynamics trajectories. Using these formulae, we improve the convergence rate of the time average with respect to the computational effort. We provide some numerical examples that show the efficiency of our scheme. When trajectories are approximated using symplectic integration schemes (such as velocity Verlet), we give error bounds that provide guidelines to choose the parameters of the computation in order to reach a given desired accuracy in the most efficient manner.
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